Cosmic distance inference from purely geometric BAO methods: Linear point standard ruler and correlation function model fitting

Leveraging the baryon acoustic oscillations (BAO) feature present in clustering 2-point statistics, we aim to measure cosmological distances independently of the underlying background cosmological model. However this inference is complicated by late-time nonlinearities that introduce model and tracer dependencies in the clustering correlation function and power spectrum, which must be properly accounted for. With this in mind, we introduce the "purely geometric-BAO," which provides a rigorous tool to measure cosmological distances without assuming a specific background cosmology. We focus on the 2-point clustering correlation function monopole, and show how to implement such an inference scheme employing two different methodologies: the linear point standard ruler (LP) and correlation-function model-fitting (CF-MF). For the first time we demonstrate how, by means of the CF-MF, we can measure very precisely the sound-horizon/isotropic-volume-distance ratio, r_d/D_V(z ¯ ) , while correctly propagating all the uncertainties. Using synthetic data, we compare the outcomes of the two methodologies, and find that the LP provides up to 50% more precise measurements than the CF-MF. Finally, we test a procedure widely employed in BAO analyses: fitting the 2-point function while fixing the cosmological and the non-linear-damping parameters at fiducial values. We find that this underestimates the distance errors by nearly a factor of 2. We thus recommend that this practice be reconsidered, whether for parameter determination or model selection.